Wednesday, September 22, 2021 — 4:00 PM EDT

Kenneth Davidson, Department of Pure Mathematics, University of Waterloo

"Strongly Peaking Representations and Compressions of Operator Systems"

We are seeking unitary invariants for d-tuples of operators and more generally for operator systems. However an operator system generally has many completely isometric representations on Hilbert space. So a strong minimality condition is required, and not all operator systems have such a representation.

An operator system is called fully compressed if the compression to any proper subspace fails to be completely isometric. We completely characterize fully compressed separable operator systems in terms of strongly peaking representations, and also in terms of the representation theory of its C*-envelope. We show that the fully compressed representation is unique up to unitary equivalence. The notion of matrix convexity underlies the main ideas.

This is joint work with Ben Passer.

This seminar will be held jointly online and in person. 

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